Proposals to expand an existing runway at Heathrow or build a second runway at Gatwick were rejected.
Transport secretary Chris Grayling said: "The step that Government is taking today is truly momentous.
"I am proud that after years of discussion and delay this Government is taking decisive action to secure the UK's place in the global aviation market - securing jobs and business opportunities for the next decade and beyond."
Grayling said expanding the west London hub will improve connectivity in the UK and with the rest of the world, supporting exports, trade and job opportunities.
He added: "This isn't just a great deal for business, it's a great deal for passengers who will also benefit from access to more airlines, destinations and flights."
The transport secretary added that the decision will be "subject to full and fair public consultation", describing it as "hugely important" for those living near the airport.
He said: "We have made clear that expansion will only be allowed to proceed on the basis of a world class package of compensation and mitigation worth up to £2.6bn, including community support, insulation, and respite from noise - balancing the benefits and the impacts of expansion."
The decision was made at a meeting of ministers in the airport sub-committee chaired by Prime Minister Theresa May.
The committee is made up of key cabinet members including chancellor Philip Hammond, business secretary Greg Clark and environment secretary Andrea Leadsom.
The Department for Transport (DfT) claimed that the new runway will bring economic benefits to passengers and the wider economy worth up to £61bn.
Officials said that up to 77,000 additional local jobs are expected to be created over the next 14 years, while the airport has committed to creating 5,000 new apprenticeships over the same period.
The Government said it will take "all necessary steps" to ensure enhanced connections within the UK, including "where appropriate, ring-fencing a suitable proportion of new slots for domestic routes."
Speaking at Downing Street, Grayling said: "This is a really big decision for this country but it's also the clearest sign, post the referendum, that this country is very clearly open for business.
"We've thought long and hard about this. The committee considered all three options. There were three very good options on the table.
"But we believe a third runway for Heathrow is the best option for our future. It's the best for the whole country to create better connectivity to the different regions of the United Kingdom and to provide the best trade links to the world."
A Heathrow spokesperson said: "We welcome the news that Heathrow is the Government's preferred site for a new runway and look forward to hearing the full details later from the Transport Secretary.
"Expansion of Heathrow is the only option that will connect all the UK to global growth, helping to build a stronger and fairer economy.
"We await the full details, but Heathrow stands ready to work with Government, businesses, airlines and our local communities to deliver an airport that is fair, affordable and secures the benefits of expansion for the whole of the UK."
The expansion is also expected to create opportunities for businesses across the UK. Speaking to BQ back in May, Heathrow chief executive John Holland-Kaye said: "With Terminal 2 all of the mechanical and electrical systems were made in the West Midlands - all of the steel came from Sheffield – the floors of the carpark came from Glasgow and the toilets came from Northern Ireland. This is a great example of how we will spread the benefits of our £60m investment right across the UK.
"A prime example of this is Hart Doors in the North East. When we built Terminal 5 they provided all of our doors and it was a great window for them to display their products worldwide. We will need a lot more of this collaboration whilst we are building as we spread the work across the UK."
Speaking about what extra airport capacity would mean for exporters, he added: "Our cargo capacity is full on many key routes, which is holding back UK exporters by forcing them to have to go by longer and more complicated routes to get to market.
"We should have the world’s best connected, most efficient and sustainable hub right here in the UK with regular flights to all of our regional airports and all other key trading centres – keeping Britain right at the heart of the global economy."